All 4 Uses

muse
in
As I Lay Dying
(Auto-generated)

...from behind his slack-faced astonishment he muses as though from beyond time, upon the ultimate outrage.
Chpt 17 *

muses = thinks (reflects deeply)
Upon the impalpable plane of it their shadows form as upon a wall, as though like sound they had not gone very far away in falling but had merely congealed for a moment, immediate and musing.†
Chpt 17
In the lantern light his face is calm, musing; slowly he strokes his hands on his rain-coated thighs in a gesture deliberate, final and composed.†
Chpt 17
Through the undergrowth it goes with a plaintive sound, a musing sound; in it the unwinded cane and saplings lean as before a little gale, swaying without reflections as though suspended on invisible wires from the branches overhead.†
Chpt 34

Definitions:

(1) (muse as in: her musings)
reflect (think) deeply on a subject -- perhaps aloud
(2) (muse as in: She was his muse)
the source of an artist's inspiration - especially a person or mythological goddess

The 9 muses were the daughters of the Greek gods Zeus & Mnemosyne. Each of the muses was thought to inspire and preside over one of the arts.
(3) (meaning too rare to warrant focus)
More rarely, muse is used as a synonym for "poet". In Shakespeare's time, muse could be used in the sense of being astonished or puzzled by something strange or unexpected.